Numerical Simulation of Turbulent Mixing inside Scale down Model of a Square Chimney for a Pool Type

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Numerical Simulation of Turbulent Mixing inside Scale down Model of a Square Chimney for a Pool Type Research Reactor Samiran Sengupta*1, P. K. Vijayan2, R. K. Singh3, A. Bhatnagar1, V. K. Raina4 Research Reactor Design & Projects Division, 2Reactor Engineering Division, 3Reactor Safety Division, 4Reactor Group, Bhabha Atomic Research Centre, Mumbai-400085, India 1

samiran_sengupta@yahoo.co.in; 2vijayanp@barc.gov.in; 3rksingh@barc.gov.in; 1abhat@barc.gov.in;

*1

vkrain@barc.gov.in

4

Abstract Numerical simulation was carried out to study the turbulent mixing behaviour of two opposite flows inside a square chimney model of a pool type research reactor. This type of chimney structure is often used for open pool type reactors to prevent mixing of core outlet water directly into the pool.

The chimney design facilitates guiding of the radioactive water from the reactor core towards the side outlet nozzles and simultaneously allows drawing water from the reactor pool through the chimney top opening. This helps to limit the radioactivity level at the pool top to a lower limit. The present work aims at studying the turbulent mixing inside a 2/9th scaled down model of chimney structure. The Reynolds numbers considered in the simulation are 1.36×106, 1.81×106, 2.26×106 and 2.72×106 which correspond to upward core flow of 12.5, 16.67, 20.83 and 25 kg/s respectively. The core bypass flow which is sucked in the downward direction varies to 0, 5, 10 and 15% of the core flow. The effects of flow ratio between the upward flow and downward flow on the mixing behaviour are analysed using PHOENICS code.

Turbulence is modelled by using the Reynolds averaged Navier Stokes (RANS) equation. The results indicate that increase in downward flow causes the jet height to decrease.

It is observed that the jet height mainly depends on the ratio of core bypass flow and core flow. The effect of change on core flow is insignificant.

Keywords CFD; Chimney; Jet Height; k-ε Model; Turbulence; Mixing; Scale Down Model

Introduction The present work is carried out to study the turbulent mixing behaviour of two opposing flows inside a 2/9th

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scaled down model of chimney of a pool type research reactor. The reactor core is cooled by upward forced flow of water through the core (Sengupta et al., 2012).

After passing through the core, the coolant becomes radioactive due to formation of various radioactive nuclides by nuclear reactions with neutrons presented in the core. Because of upward coolant velocity, it has a tendency to flow towards the pool top due to its inertia and causes increase in radiation level at the pool top. Since pool top activity should be limited during normal operation; this type of chimney structure is provided at the reactor core outlet to prevent radioactive coolant from reaching the pool top.

A typical example is High Flux Research Reactor (HFRR) being developed at BARC (Chafle et al., 2011).

A simplified flow diagram of the primary coolant system of the High Flux Research Reactor is given in FIG. 1. The hot water from core outlet is guided through the chimney and is drawn by a set of recirculating pumps through the two side outlet nozzles of the chimney. The core outlet water being radioactive is passed through delayed tanks to decay down the activity level mainly caused by N16 radionuclides and subsequently it is sent through the heat exchangers where heat is transferred to the secondary coolant. Cold primary coolant water from heat exchanger outlet is fed back to inlet plenum at the bottom of the reactor core inside the pool.

During normal operating conditions of the reactor, the bottom of the chimney sees an upward flow of hot water (49°C) from the core outlet, while a downward

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REACTOR POOL

CORE CHIMNEY

DELAY TANK

DELAY TANK

HEAT EXCHANGER

HEAT EXCHANGER

PUMPS

PUMPS

FIG. 1 SIMPLIFIED SCHEMATIC FLOW DIAGRAM OF HIGH FLUX RESEARCH REACTOR

flow from reactor pool (at 40째C) is drawn through the top opening of the chimney. Both hot upward flow from the bottom and cold downward flow from the top mix together just before the side outlet nozzles of the chimney are sucked out of the chimney with the help of recirculation pumps. The downward flow into the chimney from the pool is compensated by providing a core bypass flow discharged into the pool.

A delicate balance among the upward flow, the downward flow, nozzle inclination and height of the chimney is required to prevent the radioactive hot upward coolant mixing with the bulk pool water. In order to understand the turbulent mixing inside this chimney, an experimental flow test facility (Sengupta et al., 2012a) has been designed to simulate the mixing behaviour inside the chimney. The study aims at predicting velocity distribution inside the chimney and the upward jet height (i.e., the height where the upward flow velocity reduces to zero, with respect to the chimney reference i.e., y = 0) as well as the temperature distribution. A scaling philosophy is developed starting with the applicable governing equations and non-dimensionalising them. CFD simulations are carried out to understand the effect of these dimensionless numbers on the turbulent mixing phenomena.

Mixing Behaviour inside Chimney A simplified schematic of mixing behaviour of two opposing flows inside chimney model is shown in FIG. 2. The hot fluid from the core outlet enters into the chimney bottom inlet (1). Cold fluid from the pool enters the chimney top inlet (2). Core bypass flow is sent to the pool through two inlet lines (3, 4) to compensate for the flow entering through the chimney top inlet. Both hot upward flow (from the bottom) and cold downward flow (from the top) mix together and the mixture is sucked out of the chimney through side outlet nozzles (5, 6) with the help of pumps of the two loops of the primary coolant system.

5

6

POOL 2

1

- CHIMNEY BOTTOM INLET / REACTOR CORE OUTLET

2 - CHIMNEY TOP INLET 3 & 4 - CORE BYPASS FLOW INLET 5 & 6

3

1

- CHIMNEY SIDE OUTLET

4

FIG. 2 SIMPLIFIED MIXING FLOW DIAGRAM

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Governing Equations The basic conservation equations of mass, momentum and energy are used to determine the appropriate nondimensional parameters. Considering the fluid flow is steady and incompressible, the governing equations are given hereunder. The gravity force is considered to be acting in the (-)ve y direction as shown in FIG. 3.

vx

1 ∂p ∂vz ∂v ∂v + v y z + vz z = − ∂x ∂y ∂z ρ ∂z

+

µ  ∂ 2v z ∂ 2vz ∂ 2vz  + +   ρ  ∂x 2 ∂y 2 ∂z 2 

....(4)

As gravity force is considered to be acting in the (-) ve y-direction, pressure gradient in the pool can be expressed in terms of the following relations.

g y = −g POOL

∂p = − ρα g ∂y

Ta

35

is

temperature

Tα .

−

Y

Tin

X

Uin

∂v x ∂v y ∂v z + + =0 ∂x ∂y ∂z

…..(1)

∂v x ∂v ∂v 1 ∂p + v y x + vz x = − ∂x ∂y ∂z ρ ∂x

+

µ  ∂ vx ∂ vx ∂ vx  + +   ρ  ∂x 2 ∂y 2 ∂z 2 

∂x

∂v y ∂y

2

+ vz

∂v y ∂z

=−

µ  ∂ vy ∂ vy ∂ vy  +  2 + 2 + 2  ρ  ∂x ∂y ∂z  2

10

2

vx

∂v y ∂x

+ vy 2

vx

+ vy

 ρ ∂p + ρg y = ρ α g − ρg = ρg  α − 1 ∂y   ρ

...(7) for

low

…..(8)

∂v y ∂y

+ vz

∂v y ∂z

….(9)

= gβ (T − T∞ )

µ ∂ vy ∂ vy ∂ vy  +  2 + +  ρ  ∂x ∂y 2 ∂z 2 

2) Momentum Equations

∂v y

water

Using Eq. (9), y-momentum equation takes the following form:

1) Continuity Equation

vx

pool

ρα −1 = [1 − β (T − Tα )] = 1 + β (T − Tα ) ρ

Conservation Equations

2

at

ρ = ρα [1 − β (T − Tα )]

Wb /2

FIG. 3 GEOMETRY OF THE CHIMNEY MODEL

2

density

Using Boussinesq approximation temperature difference

D

Win

Wb /2

the

Therefore,

L

D

…..(6)

ρα

Where,

Z

…..(5)

….(2)

2

2

…(10)

3) Energy Equation

 ∂ 2T ∂ 2T   2 + 2 ∂T ∂T ∂T ∂x ∂y  …(11) vx + vy + vz =α   ∂ 2T ∂y ∂z ∂x  + 2   ∂z

1 ∂p + gy ρ ∂y

Non-Dimensionalisation

2

…(3)

The above governing equations are nondimensionalised with the following substitutions.

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X =

x ; L vx ; U in

VX =

Y=

VY =

y ; L

vy U in

Z= ;

VZ =

z L

...(12)

vz U in

…(13)

….(14)

T − Tα ξ= Tin − Tα

…(15)

ρU in L µ

1) Continuity Equation

Richardson number,

Ri =

gβ (Tin − Tα )L U in2

…(16)

Pr =

VX +

….(17)

1  ∂ 2VZ ∂ 2VZ ∂ 2VZ  + +   Re  ∂X 2 ∂Y 2 ∂Z 2 

..(18)

VX

…(19)

3) Energy Equation

  ∂ 2ξ +   2 1 ∂ξ ∂ξ ∂ξ   ∂X VX + VY + VZ = ∂X ∂Y ∂Z Re . Pr  ∂ 2 ξ ∂ 2 ξ    2 + ∂Z 2   ∂Y … .(20) Where various non-dimensional parameters are defined as follows.

...(23)

k

In addition to these above numbers, two more dimensionless numbers (Re* and Ri*) are defined to take into account the ratio between core flow and core bypass flow. Re* signifies the affect downward inertia force in suppressing the upward flow jet.

Ri* signifies the more pronouncing effect of buoyancy force against the downward forced flow.

These numbers are defined as follows.

Re * =

gβ (Tin − Tα ) L ∂VY ∂V ∂V + VY Y + VZ Y = ξ 2 ∂X ∂θ ∂Z U in

∂VZ ∂VZ ∂VZ ∂P + VY + VZ =− ∂X ∂Y ∂Z ∂Z 2 2 2 1  ∂ VZ ∂ VZ ∂ VZ  + + +   Re  ∂X 2 ∂Y 2 ∂Z 2 

......(22)

cpµ

2) Momentum Equations

∂V ∂V ∂V ∂P VX X + VY X + VZ X = − + ∂X ∂Y ∂Z ∂X 1  ∂ 2VX ∂ 2VX ∂ 2VX  + +   ∂Z 2  Re  ∂X 2 ∂Y 2

…..(21)

Prandtl number,

Where L is the characteristic length, U in is the reference inlet velocity, T α is reference temperature and T in is the inlet temperature.

∂V X ∂VY ∂VZ + + =0 ∂X ∂Y ∂Z

Reynolds number,

Re =

p P= ρU in2

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ρU in L  Wb    µ  Win 

gβ (Tin − Tα )L  Win  Ri* = U in2  Wb

…(24)

  

2

…(25)

Model Description In the present study, chimney model with 35° inclination is considered for the simulation as shown in FIG. 4. The chimney height (L) considered here is 600 mm. Side outlet nozzles are of rectangular cross section with dimension of 100 mm × 50 mm. The central chimney cross section is square with side (D) of 100 mm. The total core bypass flow is W b which is distributed through two inlet lines into the pool as shown in FIG. 3. The diameter of each inlet line is 50 mm. The core bypass flow is varied (0%, 5%, 10% and 15% of the upward flow) to analyse its effect on the jet height (H).

The CFD simulation has been carried out for the scaled down chimney model of the experimental flow test facility considering core flow of 12.5, 16.67, 20.83 and 25 kg/s. The dimensionless numbers occurring for the scale down model for which the numerical simulations are carried out in the present work are shown in TABLE 1 The results of these numerical simulations are discussed to indicate the effectiveness of downward flow in suppressing the upward flow reaching the pool top.

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TABLE 1 DIMENSIONLESS NUMBERS FOR THE SCALE DOWN CHIMNEY MODEL Re

Ri

Core bypass flow

Bypass flow entering through top of chimney (kg/s)

Downward velocity-U b (m/s)

Re*

Ri*

1.36×10 6

1.45×10 -2

0%

0.00

0.000

0.0-

∞

2

5%

0.63

0.063

6.77×10 4

5.82

3

10%

1.25

0.125

1.36×10 5

1.45

4

15%

1.88

0.188

2.03×10

0. 646

0%

0.00

0.000

0.0

6

5%

0.83

0.083

9.03×10 4

3.27

7

10%

1.67

0.167

1.81×10

5

0.815

8

15%

2.50

0.250

2.71×10 5

0.364

0%

0.00

0.000

0.0

∞

10

5%

1.04

0.104

1.13×10

11

10%

2.08

0.208

2.26×10 5

0.522

12

15%

3.13

0.313

3.39×10 5

0.233

0%

0.00

0.000

0.0

∞

14

5%

1.25

0.125

1.35×10 5

1.46

15

10%

2.50

0.250

2.72×10 5

0.362

16

15%

3.75

0.375

4.07×10

0.162

Sr. No.

Upward flow through chimney (kg/s)

Upward velocity -U in

12.5

1.25

1

5

9

(m/s)

16.67

1.667

20.83

13

1.81×10 6

2.083

25

2.26×10 6

2.500

2.72×10

6

8.15×10 -3

5.22×10 -3

3.62×10

-3

5

∞

5

5

2.10

Numerical Simulation

PLAN

600

CHIMNEY TOP OPENING

35

SIDE OUTLET NOZZLE CHIMNEY

100

CENTRAL AXIS OF CHIMNEY

SIDE VIEW

represented as

φr

ELEVATION

FIG. 4 ACRYLIC CHIMNEY MODEL

12

Numerical study of the turbulent mixing inside the chimney model is carried out using control volume based on computational fluid dynamics software PHOENICS version 3.6 (Ludwig, 2004). The solution domain is subdivided into a number of control volumes each of which is associated with a grid point, where the scalar variables such as pressure, temperature, concentration etc. are stored. The control volumes for the velocity are staggered in relation to the control volumes for the scalar variables. The fluid (water) is assumed to be incompressible and Newtonian with constant fluid properties. The convection terms in the momentum and energy equations are discretised using the hybrid scheme. The discretised equations are solved in a semi-coupled manner by a variant of the well-known simple algorithm. The solution is considered converged when the following criterion has been met for all dependent variables between sweep n and n+1. Reference value is

max

.

φ n +1 − φ n ≤ 10− 3 φr

….(26)

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Whole field residuals are also checked to ensure that the converged solution satisfies the governing equations within a prescribed error.

Turbulence Modelling To simulate turbulent flow, various models (Rodi, 1993) are developed by researchers to determine the eddy viscosity (υ t ) of which the standard k-ε model has been widely used due to its robustness, economy and reasonable accuracy for various industrial flow problems. The standard k- ε model was proposed by Harlow and Nakayama (1968). PHOENICS provides the standard high Reynolds number form of k- ε model as presented by Launder and Spalding (1974). It is a semi-empirical model and the derivation of the two additional transport equations for the turbulent kinetic energy, k and the turbulence dissipation rate, ε relies on phenomenological considerations and empiricism.

The eddy viscosity is computed as a function of k and ε as follows.

υt = cµ

k2

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turbulence dissipation rate (ε) are prescribed at the inlet. The k value is represented in terms of the turbulence intensity which typically falls in the range of 1% to 5%. In the simulation the turbulence intensity is assumed to be 5%. The turbulence dissipation rate (ε) depends on turbulent kinetic energy (k) and mixing length (l m ) as shown in the following relation. Mixing length is assumed to be 10% of the characteristic inlet dimension (i.e., hydraulic radius for the inlet pipe) for all these simulations.

ε = 0.1643

k 3/ 2 lm

….. (28)

At the outlet, constant pressure boundary condition is applied. At each wall, no-slip boundary condition is imposed. Temperature at inlet of the core flow is specified to be 49°C. For core bypass flows at the inlet of two nozzles, temperature is specified to be 40°C.

…(27)

ε

Values of constants in the standard k-ε model used in the simulation are shown in TABLE 1, TABLE 2 values of constants for the turbulence model Constan ts

cµ

c 1ε

c 2ε

σk

σε

Values

0.09

1.44

1.92

1.0

1.3

(a) Mesh in x-z plane

Meshing The geometrical model considered for computation has the same dimensions of the chimney model planned for the experiments. However, free surface modeling at the interface between pool water and air at the top is not modelled considering larger pool water depth above the chimney top. FIG. 5 depicts cross section of the computation domain (750 mm x 1000 mm x 250 mm) in the x-z and x-y plane showing the mesh for the entire domain. Simulations are carried out using two different mesh sizes - (110 × 200 × 40) and (120 × 220 × 45). No significant differences are observed.

Boundary Conditions At the inlet, the flow rate of the fluid is specified considering uniform velocity profile and the direction of flow velocity is defined normal to the boundary. The values of the turbulent kinetic energy (k) and

(b) Mesh in x-y plane FIG. 5 MESH USED FOR COMPUTATION DOMAIN

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Wall Treatment Flows are significantly affected by the presence of wall boundary. Traditionally there are two approaches to modelling the near wall region. In one approach, the molecular viscosity affected inner region (i.e., viscous sublayer and buffer layer) is not resolved and instead semi-empirical formula (i.e., wall function) is used to bridge the viscosity affected region between the wall and the fully turbulent region. In the other approach, turbulence models are modified to enable the viscosity affected region to be resolved all the way to the wall, including viscous sublayer. Thus, a very fine mesh is required near the wall for this approach. Due to limitation of large number of mesh points, wall function approach is employed in the present work.

Literature Survey Turbulent mixing study for hot and cold streams has been reported by various researchers. Wang and Mujumdar (2007) carried out numerical simulation for dual-inlet inline mixer where two opposing air jets (i) a cold jet (304 K) and (ii) a hot jet (315 K) were mixed from the side onto the main pipe. Standard k- ε turbulence model was selected to model the turbulent mixing (Re=35000). Experimental work of mixing of cold water with hot water in a Tee junction with a 90° bend upstream was reported by Hosseini, Yuki and Hashizume (2008). Mixing behaviour of hot and cold water jets in a Tee junction was experimentally and numerically investigated by Kamide, et. al (2009) for maximum Re of 4.35×105 for the main flow. The branch flow corresponds to maximum Reynolds number of about 75000. The experiment of Naik-Nimbalkar et. al (2010) involved mixing of cold water and hot water in a T-junction test section. Three dimensional CFD simulations were also reported using standard k–ε turbulence model for comparison with the experimental results. Applicability of PHOENICS code for turbulent mixing studies has been reported by Sengupta et. al (2013) in their previous work.

procedure is adopted to find these parameters for the core flow of 16.66, 20.83 and 25 kg/s. Finally nondimensionalisation of the results is done to bring them in similar platform to compare the results with respect to the dimensionless numbers.

Core flow – 12.5 kg/s Upward flow (W in ) through the chimney bottom inlet is assumed to be 12.5 kg/s. The Reynolds number corresponding to this flow is 1.36×106. The temperature at the inlet is 49°C. The core bypass flow varieS to 0, 0.63, 1.25 and 1.88 kg/s respectively to estimate the effect of core bypass flow on the mixing characteristics inside the chimney. The inlet temperature of bypass flow (W b ) is 40°C. 1) Velocity distribution for 0% core bypass The flow pattern inside the chimney with no core bypass (i.e., 0% of core flow) is shown in FIG. 6 to FIG. 7. FIG. 6(a) and 6(b) show the velocity distribution in the x-y plane (at z = 0.0) and y-z plane (at x = 0.0) respectively. In this case, no flow is sent to the pool and therefore, the core flow of 12.5 kg/s is diverted into two side outlet nozzles as shown in FIG. 6(a). The velocity vectors in the outlet nozzles show direction of velocity and its magnitude. It is observed that in the vertical legs, velocity is more towards the outer side of the leg.

This is due to change in direction of flow from inclined leg to vertical leg.

Reslts and Discussion Based on the methodology described above, all the numerical simulations (mentioned in TABLE 1) were carried out. The flow pattern and temperature distribution contours for the case with core flow of 12.5 kg/s are described in details in the following subsections. Basic objectives of these simulations are to find out the jet height and temperature front height, which is explained for this case. Subsequently, similar

14

(a) x-y plane

(b) y-z plane

FIG. 6 VELOCITY DISTRIBUTION FOR CORE FLOW OF 12.5 KG/S WITH 0% BYPASS

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Through central square chimney region, the upward velocity is observed to a certain height in FIG. 6(a). The water jet with two vortices is observed in FIG. 6(b). To clearly observe the flow pattern inside the central square chimney region, velocity vector plots in x-y plane and y-z plane are shown in FIG. 7(a) and FIG. 7(b) respectively. The results are shown upto the top (i.e., y = 0.6 m) of the chimney. In the lower most region of FIG. 7(a), the velocity vectors show upward tendency along with direction towards two side outlet openings. Above this region, asymmetrical circulation with lower velocity is observed with longer length. However, FIG. 7(b) shows how the upward central jet takes turn symmetrically from both sides to become downward. It is also observed in FIG. 7(b) that downward flow through the top opening of the chimney takes place in the central region. Since there is no net flow provided for the top opening of the chimney, upward flow takes place through the peripheral region in order to maintain the over all balance of flow. This upward flow tendency through the top opening of the chimney is not acceptable because it will lead to reaching radioactive water from the core outlet to the pool.

Therefore, additional bypass flow cases are analysed to observe their effect on keeping the radioactive water well within the chimney region without allowing it to go towards the pool.

(a) x-y plane

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shown in FIG. 8(a) and 8(b) respectively. In FIG. 8(a), it is observed that from the bottom through two nozzles, bypass flow is sent to the tank.

Because of this additional flow through the chimney top opening in the downward direction, velocity in the side outlet nozzles increases as shown in FIG. 8(a). In this case also the flow velocities in the vertical leg are more towards the outer side than that towards the inner side. In the central square chimney region, downward flow is observed. In FIG. 8(b), the upward velocity jet contour is observed. The jet height is found to be less than that observed for 0% core bypass case.

Length of the two vortices is also observed to be less. This is clearly visible in the velocity vector plot of y-z plane as shown in FIG. 9(b). When FIG. 7(b) and FIG. 9(b) are compared, the extent of the upward velocity region is also observed to be reduced. The downward flow velocity from the top of the chimney throughout the whole square cross section is observed in both FIG. 9(a) and FIG. 9(b).

Therefore, in this case no radioactive water is able to reach the pool top. Now, the extent of suppression of upward jet due to increase in core bypass flow is further analysed by varying the bypass to 10% and 15%.

(b) y-z plane

FIG. 7 VELOCITY VECTOR IN CENTRAL CHIMNEY FOR CORE FLOW OF 12.5 KG/S WITH 0% BYPASS (FROM y=0.2 TO 0.6 M)

2) Velocity distribution with 5% core bypass: The velocity contours in x-y plane and y-z plane for 0.63 kg/s bypass flow case (i.e., 5% of core flow) are

(a) x-y plane

(b) y-z plane

FIG. 8 VELOCITY DISTRIBUTION FOR CORE FLOW OF 12.5 KG/S WITH 5% BYPASS

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(a) x-y plane

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(b) y-z plane

FIG. 9 VELOCITY VECTOR IN CENTRAL CHIMNEY FOR CORE FLOW OF 12.5 KG/S WITH 5% BYPASS (FROM y=0.2 TO 0.6 M)

3) Velocity distribution with 10%,15% core bypass: The results for core bypass of 1.25 kg/s (i.e., 10% of core flow) and 1.88 kg/s (i.e., 15% of core flow) are shown in FIG. 10 to FIG. 13. With increase in core bypass flow, the velocity contour plots of x-y plane show the increase in velocity and their distribution near the bottom region of the pool of FIG. 10(a) and FIG. 12(a). This additional bypass flow when sucked in through the top of the chimney suppresses the upward velocity as observed in FIG. 10(b) and 12(b).

(a) x-y plane

(b) y-z plane

FIG.11 VELOCITY VECTOR IN CENTRAL CHIMNEY FOR CORE FLOW OF 12.5 KG/S WITH 10% BYPASS (FROM y=0.2 TO 0.6 M)

(a) x-y plane

(b) y-z plane

FIG.12 VELOCITY DISTRIBUTION FOR CORE FLOW OF 12.5 KG/S WITH 15% BYPASS

(a) x-y plane

(b) y-z plane

FIG.10 VELOCITY DISTRIBUTION FOR CORE FLOW OF 12.5 KG/S WITH 10% BYPASS

16

It is observed from the magnitude of the velocity vector plots of FIG. 11 and FIG. 13 that the upward velocity at y=0.2 m is reduced as the downward velocity through the top chimney is increased. This is because of the higher downward momentum of larger bypass flow, the core outlet flow gets diverted towards the side outlet nozzles more effectively and thereby reducing the upward jet velocity. This in turn causes the jet height to reduce.

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In order to quantify the jet height, the centre line velocity of the chimney is plotted against the height of the chimney.

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It is observed from FIG. 14 that velocity decreases and reaches to zero value. Beyond this point velocity becomes negative, i.e., downward velocity is observed. The value of y where upward velocity (v y ) is zero is defined as the jet height. The jet height for 0% bypass flow is 0.264 m and for 15% case, which is 0.213 m. It is observed from the figure that jet height decreases with the increase in core bypass flow.

5) Temperature Distribution

(a) x-y plane

(b) y-z plane

FIG.13 VELOCITY VECTOR IN CENTRAL CHIMNEY FOR CORE FLOW OF 12.5 KG/S WITH 15% BYPASS (FROM y=0.2 TO 0.6 M)

4) Centre line height

velocity variation with chimney

The upward velocity (v y ) variation along the height of the chimney is shown in FIG. 14 for 0%, 5%, 10% and 15% core bypass flow cases. The upward flow velocity at the bottom inlet of the chimney (at y = -0.1 m) is about 1.25 m/s.

1.5 Core flow = 12.5 kg/s 0 % bypass 5 % bypass 10 % bypass 15 % bypass

vy (m/s)

1.0

0.5

0.0

-0.5 -0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

y (m) FIG. 14 CENTRE LINE UPWARD VELOCITY VARIATION WITH CHIMNEY HEIGHT (Re = 1.36×10 6 , Ri = 1.45×10 -2)

At y =0.0 m, the side outlet nozzle opening starts.

With further increase in y, flow moves towards side outlet nozzles and upward velocity decreases. Up to y = 0.13 m, the velocity variation is the same for all the bypass cases. At higher value of y, the velocity variation depends on the core bypass flow.

When core bypass flow is 0%, the hot core outlet water at 49°C moves upward through the peripheral region as explained in previous subsection (1) and it is observed that the pool temperature stabilises at 49°C considering steady state condition. This indirectly indicates that pool water will attain the radioactivity level of core outlet water if it is assumed that temperature is acting as an indirect way of radiotracer. The temperature contour plots for 5%, 10% and 15% core bypass flow are shown in FIG. 15. It is observed that with the increase in bypass flow, the temperature at the vertical leg of the side outlet nozzles decreases. The temperature pattern shows that even at the outlet section, the flow is not thermally developed as shown in FIG. 15a(i), b(i) and c(i). The variation of temperature form the inner side face to the outer side face is more when bypass flow is more. This is because more amount of cold fluid (at 40°C) entering through the chimney moves out of the chimney preferentially towards the inner side face of the chimney. Hotter water (at 49°C) moves out of the chimney preferentially towards the outer side face of the chimney.

It is also observed that hot water penetration into the chimney becomes less with the increase in core bypass flow. Due to suck of pool water through the top of the chimney, pool water front (at 40°C) reaches inside chimney which restricts hot core outlet temperature to propagate further in the upward direction. The maximum depth up to which the temperature front of pool water will reach can be thought as the location above which hot water of core outlet does not have any effect.

The value of y at this location is defined as the temperature front height. From the figures, it is observed that with the increasein bypass flow the temperature front height decreases. To quantify these values for various cases, centre line temperature variation is plotted along the height of the chimney.

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Studies in Chemical Process Technology (SCPT) Volume 1 Issue 1, February 2013

a(i)

a(ii)

b(i)

b(ii)

c(i)

c(ii)

FIG. 15 TEMPERATURE CONTOURS - CORE FLOW 12.5 KG/S, BYPASS (a) 5% (b) 10% (c) 15% (i) CONTOUR PLOT IN x-y PLANE (ii) CONTOUR PLOT IN y-z PLANE

6) Centre line temperature chimney height

variation

with

The water temperature variation along the central axis of the square chimney with respect to the chimney height is shown in FIG. 16. At the entry of the bottom inlet of chimney, the water temperature is 49°C. When core bypass flow is 0%, this 49°C temperature is observed throughout the chimney height. Up to a height, y = 0.17, this temperature is observed for other bypass flow cases. At higher height, the temperature depends on the core bypass flow. When core bypass flow is more, the temperature drops at a faster rate. With 5% core bypass flow, temperature front height is 0.268 m. ith the increase in bypass flow to 15%, the temperature front height reduces to 0.237 m.

Effect of Core flow on Velocity distribution To understand the effect of core flow variation on velocity distribution inside the chimney, core flow varies to 16.66, 20.83 and 25 kg/s. The Reynolds numbers corresponding to these core flows are 1.81×10 6, 2.26×10 6 and 2.72×10 6 respectively. FIG. 17 shows the velocity variation with the chimney height for core flow of 16.66 kg/s. At the bottom of the chimney flow velocity is about 1.66 m/s, which gradually decreases with chimney height. For 0 % bypass case, the velocity becomes zero at y = 0.266 m and for 15% bypass flow, it occurs at y = 0.212 m.

2.0

50

1.0

vy (m/s)

49 48 Core flow = 12.5 kg/s 0 % bypass 5 % bypass 10 % bypass 15 % bypass

47

T (oC)

46 45

0.5

0.0

44 43

-0.5 -0.1

42 40 39 -0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

y (m)

41

0.0

0.1

0.2

0.3

0.4

0.5

0.6

y (m)

FIG.16 WATER CENTRE LINE TEMPERATURE VARIATION WITH CHIMNEY HEIGHT (Re = 1.36×10 6 , Ri = 1.45×10 -2)

18

Core flow = 16.66 kg/s 0 % bypass 5 % bypass 10 % bypass 15 % bypass

1.5

FIG.17 CENTRE LINE UPWARD VELOCITY VARIATION WITH CHIMNEY HEIGHT (Re = 1.81×10 6 , Ri = 8.15×10 -3)

FIG. 18 and 19 show the upward velocity variation along the central axis of the chimney for core flow of 20.83 and 25 kg/s respectively. For these cases, the

Studies in Chemical Process Technology (SCPT) Volume 1 Issue 1, February 2013

similar trend of results are observed. For 20.83 kg/s core flow, the chimney flow velocity reduces from 2.08 m/s (at bottom y= -0.1 m) to zero value at y = 0.266 m for 0% bypass flow and y = 0.211 m for 15% bypass flow. For 25 kg/s core flow, the inlet velocity of 2.5 m/s reduces to zero velocity at y = 0.266 m for 0 % core bypass flow and 0.210 m for 15 % bypass flow. It is also observed that downward velocity through top of the chimney increases with the increase in inlet velocity, when similar bypass flow % is considered.

2.5

vy (m/s)

1.5 1.0 0.5 0.0 -0.5 -0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

y (m) FIG.18 CENTRE LINE UPWARD VELOCITY VARIATION WITH CHIMNEY HEIGHT (Re = 2.26×10 6 , Ri = 5.22×10 -3)

3.0 2.5

Core flow = 25 kg/s 0 % bypass 5 % bypass 10 % bypass 15 % bypass

vy (m/s)

2.0 1.5

observed that for all theses cases the trend of temperature variation is similar. Hot water at 49°C mixes with the cold water of the pool at 40°C inside the chimney in which case core bypass flow is provided. For 5% core bypass flow, temperature front height is observed to be 0.267 m, 0.268 m, 0.270 m for core flow of 16.66, 20.83 and 25 kg/s respectively. For 15% core bypass flow, the temperature front height reduces to 0.237 m, .237 m, 0.235 m respectively. Therefore, the pool temperature front height decreases with the increase in core bypass flow for these cases.

Non-dimensionalisation of output results

Core flow = 20.83 kg/s 0 % bypass 5 % bypass 10 % bypass 15 % bypass

2.0

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1.0

To consolidate all the above results, the output results were represented in the non-dimensional form. The velocity is non-dimensionalised with the reference inlet velocity (U in ) at the bottom inlet of the chimney.

The chimney distance is nondimensionalised with respect to the chimney height (L). The dimensionless velocity variation along the central axis of the chimney with dimensionless chimney distance is shown in FIG. 23. It is clearly observed from the figure that the trend of results follows the same pattern for the Reynolds number range covered in the analysis in which case the bypass to core flow ratio (W b /W in ) is kept the same.

Similarly dimensionless temperature variation with respect to dimensionless distance is shown in FIG. 24.

Temperature is non-dimensionalised considering pool temperature as the reference temperature. Here also, it is observed that temperature variation follows the same behaviour once the bypass to core flow ratio is maintained for the range of Reynolds number considered in the simulations.

50

0.5

49 48

0.0

Core flow = 16.66 kg/s 0 % bypass 5 % bypass 10 % bypass 15 % bypass

47 46

0.0

0.1

0.2

0.3

0.4

0.5

0.6

y (m)

T (oC)

-0.5 -0.1

45 44 43 42

FIG.19 CENTRE LINE UPWARD VELOCITY VARIATION WITH CHIMNEY HEIGHT (Re = 2.72×10 6, Ri = 3.62×10 -3)

41

Effect of Core flow on Temperature distribution

39 -0.1

Temperature variation along the central axis of the chimney for core flow of 16.66, 20.83 and 25 kg/s is shown in FIG. 20, 21 and 22 respectively. It is

40 0.0

0.1

0.2

0.3

0.4

0.5

0.6

y (m)

FIG.20 WATER CENTRE LINE TEMPERATURE VARIATION WITH CHIMNEY HEIGHT (Re = 1.81×10 6 , Ri = 8.15×10 -3)

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50

50

49

49

48

45

46

44

45 44

43

43

42

42

41

41

40

40

39 -0.1

0.0

0.1

0.2

0.3

0.4

0.5

Core flow = 25 kg/s 0 % bypass 5 % bypass 10 % bypass 15 % bypass

47

T (oC)

46

T (oC)

48

Core flow = 20.83 kg/s 0 % bypass 5 % bypass 10 % bypass 15 % bypass

47

39 -0.1

0.6

0.0

0.1

0.2

0.4

0.5

0.6

FIG.22 WATER CENTRE LINE TEMPERATURE VARIATION WITH CHIMNEY HEIGHT (Re = 2.72×10 6, Ri = 3.62×10 -3)

FIG.21 WATER CENTRE LINE TEMPERATURE VARIATION WITH CHIMNEY HEIGHT (Re = 2.26×10 6 , Ri = 5.22×10 -3)

1.0

Re=1.36 x 106, Re*=0.0 6 4 Re=1.36 x 10 , Re*=6.77 x 10 Re=1.36 x 106, Re*=1.36 x 105 6 5 Re=1.36 x 10 , Re*=2.03 x 10 6 Re=1.81 x 10 , Re*=0.0 Re=1.81 x 106, Re*=9.03 x 104 Re=1.81 x 106, Re*=1.81 x 105 6 Re=1.81 x 10 , Re*=2.71 x 105 6 Re=2.26 x 10 , Re*=0.0 Re=2.26 x 106, Re*=1.13 x 105 Re=2.26 x 106, Re*=2.26 x 105 6 Re=2.26 x 10 , Re*=3.39 x 105 6 Re=2.72 x 10 , Re*=0.0 6 5 Re=2.72 x 10 , Re*=1.35 x 10 Re=2.72 x 106, Re*=2.72 x 105 6 5 Re=2.72 x 10 , Re*=4.07 x 10

0.8

VY (dimensionless velocity)

0.3

y (m)

y (m)

0.6

0.4

0.2

0.0

-0.2 0.0

0.2

0.4

0.6

0.8

1.0

Y (dimensionless distance) FIG.23 NON-DIMENSIONAL CENTRE LINE VELOCITY VARIATION WITH NON-DIMENSIONAL CHIMNEY HEIGHT

1) Variation of Jet height with Reynolds number

20

YH (dimensionless height of water jet)

As is observed form FIG. 23 that the dimensionless velocity variation is more dependent on the bypass to core flow ratio than that of the core flow only. Bypass to core flow ratio is also equals to Re*/Re. From FIG. 23, dimensionless height (Y H ) of water jet is predicted by considering the value of Y which corresponds to V y equal to zero. FIG. 25 shows the variation of Y H with the Reynolds number (Re) corresponding to the core flow. It is clear from the results that variation of Reynolds number has little effect on the dimensionless jet height. However, bypass to core flow ratio (Re*/Re) has significant effect on the dimensionless jet height.

1.0 Re* / Re = Re* / Re = Re* / Re = Re* / Re =

0.8

0.00 0.05 0.10 0.15

0.6

0.4

0.2

0.0 1.2x106

1.6x106

2.0x106

2.4x106

2.8x106

Reynolds number (Re) FIG.25 DIMENSIONLESS JET HEIGHT VARIATION WITH REYNOLDS NUMBER (Re)

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1.0 6

Re=1.36 x 10 , Re*=0.0 Re=1.36 x 106, Re*=6.77 x 104 6 5 Re=1.36 x 10 , Re*=1.36 x 10 6 5 Re=1.36 x 10 , Re*=2.03 x 10 6 Re=1.81 x 10 , Re*=0.0 6 4 Re=1.81 x 10 , Re*=9.03 x 10 6 5 Re=1.81 x 10 , Re*=1.81 x 10 Re=1.81 x 106, Re*=2.71 x 105 Re=2.26 x 106, Re*=0.0 6 5 Re=2.26 x 10 , Re*=1.13 x 10 Re=2.26 x 106, Re*=2.26 x 105 6 5 Re=2.26 x 10 , Re*=3.39 x 10 6 Re=2.72 x 10 , Re*=0.0 Re=2.72 x 106, Re*=1.35 x 105 6 5 Re=2.72 x 10 , Re*=2.72 x 10 Re=2.72 x 106, Re*=4.07 x 105

両 (dimensionless temperature)

0.8

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Y (dimensionless distance) FIG.24 NON-DIMENSIONAL CENTRE LINE TEMPERATURE VARIATION WITH NON-DIMENSIONAL CHIMNEY HEIGHT

2) Variation of Temperature Front height with Reynolds number

YT (dimensionless height of temperature front)

Dimensionless temperature front height is predicted from FIG. 24. The minimum dimension-less distance where dimensionless temperature (両) becomes zero is considered to be dimensionless temperature front height (Y T ). Variation of Y T with Reynolds number of core flow is shown in FIG. 26.

It is observed that Variation of Y T with Reynolds number is almost negligible. However, bypass to core flow ratio (Re*/Re) has significant effect on the dimensionless temperature front height.

1.0 Re* / Re =0.05 Re* / Re =0.10 Re* / Re =0.15

0.8

0.6

0.4

0.2

Conclusions The study of turbulent mixing behaviour of two opposite flows inside the 2/9th scale down square chimney model of a pool type research reactor is described. A case considering no core bypass flow is simulated, which shows that upward flow velocity exists in the peripheral region at the chimney top opening. This is not acceptable because radioactive core outlet water will reach the pool top for this case.

The results of the simulations for 5%, 10% and 15% core bypass flow show that jet height decreases with the increase in core bypass flow. The effect of variations in core flow has been also analysed. It was observed that jet height as well as pool temperature front height does not change significantly with the change in core flow in which case bypass to core to flow ratio is maintained. Non-dimensionalisation of the results shows that velocity distribution and temperature distribution inside the chimney is similar.

Dimensionless jet height and temperature front height remains almost constant and independent of the Reynolds number of the core flow.

ACKNOWLEDGMENT

0.0 1.2x106

1.6x106

2.0x106

2.4x106

2.8x106

Reynolds number (Re) FIG.26 DIMENSIONLESS TEMPERATURE FRONT HEIGHT VARIATION WITH REYNOLDS NUMBER (Re)

The Authors would like to thank Shri K. Sasidharan, Former Head RRDPD and Shri R. C. Sharma, Head RRSD for their valuable guidance and continuous support for carrying out the present work.

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REFERENCES

type research reactor,” Annals of Nuclear Energy, Vol. 51,

B. E. Launder, and D.B. Spalding, “The numerical computation of turbulent flows,” Comp. Math. In Appl.

2013.

V. S. Naik-Nimbalkar, A. W. Patwardhan, I. Banerjee, G. Padmakumar, and G. Vaidyanathan, “Thermal mixing in

Mech. & Eng., Vol 3, 1974.

T- junctions,” Chem. Eng. Sci., Vol. 65, 2010.

F. H. Harlow, and P.I. Nakyama, “Transport of turbulent energy decay rate,” LA-3854, Los Alamos Science Lab, U. California, USA, 1968.

Nomenclature cp

specific heat at constant pressure (J/kg/ K)

D

side of square chimney (m)

numerical analyses for evaluation of thermal striping,”

g

acceleration due to gravity (m/s2)

Nuclear Engineering and Design, Vol 239, 2009.

H

jet height (m)

H. Kamide, M. Igarashi, S. Kawashima, N. Kimura, and K. Hayashi, “Study on mixing behavior in a tee piping and

J. C. Ludwig, “Concentration, Heat and Momentum Limited (CHAM),” POLIS: Phoenics On-line Information System, London. 2004 Rodi, Wolfgang, “Turbulence models and their application

H T temperature front height (m) k

turbulent kinetic energy (J/kg)

l m mixing length (m)

in hydraulics – a state of the art review,” 3rd edition,

L

length of chimney (m)

Rotterdam, Netherlands, 1993.

p

pressure (Pa)

S. J. Wang, and A. S. Mujumdar, “Flow and mixing

P

non-dimensional pressure, p/(ρU2 in )

characteristics of multiple and multi-set opposing jets,”

R

mass flow ratio=W b /W in =Re*/Re

Chemical Engineering and Processing, Vol. 46, 2007.

S. M. Hosseini, K.Yuki, and H. Hashizume, “Classification of turbulent jets in a T-junction area with a 90-deg bend

Ri Richardson number

upstream,” Int. Journal of Heat and Mass Transfer, Vol.

T

temperature (K)

51, 2008.

U

reference velocity (m/s)

S. B. Chafle, Samiran Sengupta, P. Mukherjee, K. Sasidharan, and

V.

K.

Raina,“High

Flux

Research

Reactor,”

Peacefulatom 2009, Thematic volume Reactor systems & Applications, pp. 195-200, Jan., 2011.

Samiran Sengupta, Tej Singh, A. Bhatnagar, and V. K. Raina,

U b bypass velocity= W b /(ρD2) (m/s) U in inlet velocity= W in /(ρD2) (m/s) v

fluid velocity (m/s)

V

non-dimension fluid velocity (v/U in )

“Steady state thermal hydraulic analysis for a pool

W mass flow (kg/s)

type

y

high

flux

research

reactor,” 39th National

Conference on Fluid Mechanics and Fluid Power, SVNIT Surat, India, FMFP2012-12, Dec., 13-15, 2012.

Samiran Sengupta, P. K. Vijayan, A. Bhatnagar, and V. K.

vertical height (m)

Y non-dimensional vertical height (y/L) Symbols

Raina, “Experimental flow test facility to study the

β volumetric expansion coefficient (/K)

turbulent mixing inside the chimney model of a pool

ε turbulent kinetic energy dissipation rate (W/kg)

type

ρ fluid density (kg/m3)

research

reactor,” 39th National Conference on

Fluid Mechanics and Fluid Power, SVNIT Surat, India, FMFP2012-34, Dec., 13-15, 2012a.

Samiran Sengupta; P. K. Vijayan, K. Sasidharan, and V. K.

22

Re Reynolds number

μ viscosity (Ns/m2) υ kinematic viscosity (m2/s)

Raina, “A numerical study of flow and mixing

υ t eddy viscosity (m2/s)

characteristics inside the chimney structure of a pool

ξ dimensionless temperature, (T-T α )/( (T in -T α )

Studies in Chemical Process Technology (SCPT) Volume 1 Issue 1, February 2013

Subscripts b bypass in inlet x x-direction y y-direction z z-direction

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Samiran Sengupta was born in the year 1969 in Medinipur, West Bengal, India. He did his Bachelor Degree in Mechanical Engineering from Jadavpur University, Kolkata in the year 1990. He completed his M.E. in Mechanical Engg. from Indian Institute of Science (IISc), Bangalore in 1992. He is from the 1st batch of orientation course for engineering postgraduates (OCEP) from BARC Training School, Mumbai.

His major field of interest is fluid flow and heat transfer. He is involved in design of process systems of nuclear research reactor. He is also involved in safety analyses as well as design safety review of nuclear reactors.

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